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{{cosmology}}The accelerating expansion of the universe is the observation that the expansion of the universe is such that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.NEWS, Overbye, Dennis, Dennis Overbye, Cosmos Controversy: The Universe Is Expanding, but How Fast?,weblink 20 February 2017, The New York Times, 21 February 2017, WEB, Scharping, Nathaniel, Gravitational Waves Show How Fast The Universe is Expanding,weblink 18 October 2017, Astronomy (magazine), Astronomy, 18 October 2017, WEB, Weaver, Donna, Villard, Ray, Measuring universe expansion reveals mystery â Is something unpredicted going on in the depths of space?,weblink 11 March 2018, Earth & Sky, 11 March 2018, WEB,weblink Is the universe expanding faster than the speed of light?, The accelerated expansion was discovered during 1998, by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration.NEWS,weblink Nobel physics prize honours accelerating universe find, BBC News, 2011-10-04, WEB,weblink The Nobel Prize in Physics 2011, Nobelprize.org, 2011-10-06, JOURNAL, Peebles, P. J. E., Ratra, Bharat, The cosmological constant and dark energy, 2003, Reviews of Modern Physics, astro-ph/0207347, 75, 2, 559â606, 10.1103/RevModPhys.75.559, 2003RvMP...75..559P, The idea was that as type 1a supernovae have almost the same intrinsic brightness (a standard candle), and since objects that are further away appear dimmer, we can use the observed brightness of these supernovae to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred.See also Hubble law, which established that the further an object is from us, the faster it is receding. The unexpected result was that objects in the universe are moving away from another at an accelerated rate. Cosmologists at the time expected that recession velocity would always be decelerating to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery.BOOK, Cosmology, Steven, Weinberg, Oxford University Press, 2008, 9780198526827, Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.The accelerated expansion of the universe is thought to have begun since the universe entered its dark-energy-dominated era roughly 5 billion years ago.JOURNAL, Frieman, Joshua A., Turner, Michael S., Huterer, Dragan, 2008, Dark Energy and the Accelerating Universe, Annual Review of Astronomy and Astrophysics, 46, 1, 385â432, 0803.0982, 2008ARA&A..46..385F, 10.1146/annurev.astro.46.060407.145243, {{refn |1= Frieman, Turner & Huterer (2008) p. 6: "The Universe has gone through three distinct eras: radiation-dominated, {{math|z â³ 3000}}; matter-dominated, {{math|3000 â³ z â³ 0.5}}; and dark-energy-dominated, {{math|z â² 0.5}}. The evolution of the scale factor is controlled by the dominant energy form: {{math|a(t) â t2/3(1 + w)}} (for constant {{mvar|w}}). During the radiation-dominated era, {{math|a(t) â t1/2}}; during the matter-dominated era, {{math|a(t) â t2/3}}; and for the dark energy-dominated era, assuming {{math|w {{=}} â1}}, asymptotically {{math|a(t) â exp(Ht)}}."p. 44: "Taken together, all the current data provide strong evidence for the existence of dark energy; they constrain the fraction of critical density contributed by dark energy, 0.76 Â± 0.02, and the equation-of-state parameter, {{mvar|w}} â â1 Â± 0.1 (stat) Â± 0.1 (sys), assuming that {{mvar|w}} is constant. This implies that the Universe began accelerating at redshift {{math|z â¼}} 0.4 and age {{math|t â¼}} 10 Gyr. These results are robust â data from any one method can be removed without compromising the constraints â and they are not substantially weakened by dropping the assumption of spatial flatness."|group="notes"}}Within the framework of general relativity, an accelerated expansion can be accounted for by a positive value of the cosmological constant {{mvar|Î}}, equivalent to the presence of a positive vacuum energy, dubbed "dark energy". While there are alternative possible explanations, the description assuming dark energy (positive {{mvar|Î}}) is used in the current standard model of cosmology, which also includes cold dark matter (CDM) and is known as the Lambda-CDM model.

Background

{{Nature timeline}}{{further|Cosmological constant|Lambda-CDM model|Hubble's law|FriedmannâLemaÃ®treâRobertsonâWalker metric|Friedmann equations}}In the decades since the detection of cosmic microwave background (CMB) in 1965,JOURNAL, Penzias, A. A., Wilson, R. W., 1965, A Measurement of Excess Antenna Temperature at 4080 Mc/s, The Astrophysical Journal, 142, 1, 419â421, 1965ApJ...142..419P, 10.1086/148307, the Big Bang model has become the most accepted model explaining the evolution of our universe. The Friedmann equation defines how the energy in the universe drives its expansion.

where {{mvar|Îº{edih} represents the curvature of the universe, {{math|a(t)}} is the scale factor, {{mvar|Ï}} is the total energy density of the universe, and {{mvar|H}} is the Hubble parameter.JOURNAL, Nemiroff, Robert J., Robert J. Nemiroff, Patla, Bijunath, Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations, American Journal of Physics, 76, 3, 265â276, 10.1119/1.2830536, astro-ph/0703739, 2008AmJPh..76..265N, 2008, We define a critical density

where the four currently hypothesized contributors to the energy density of the universe are curvature, matter, radiation and dark energy.BOOK, Lapuente, P., Baryon Acoustic Oscillations, Dark Energy: Observational and Theoretical Approaches, Cambridge, UK, Cambridge University Press, 2010, 978-0521518888, 2010deot.book.....R, Each of the components decreases with the expansion of the universe (increasing scale factor), except perhaps the dark energy term. It is the values of these cosmological parameters which physicists use to determine the acceleration of the universe.The acceleration equation describes the evolution of the scale factor with time

frac{ddot{a}}{a}=-frac{4{pi}G}{3}left( rho + frac{3P}{c^2} right)

where the pressure {{mvar|P}} is defined by the cosmological model chosen. (see explanatory models below)Physicists at one time were so assured of the deceleration of the universe's expansion that they introduced a so-called deceleration parameter {{math|q0}}.BOOK, Introduction to Cosmology, Ryden, Barbara, San Francisco, CA, Addison Wesley, 2003, 978-0-8053-8912-8, {{Page needed |date=September 2016}} Current observations indicate this deceleration parameter being negative.

Relation to inflation

According to the theory of cosmic inflation, the very early universe underwent a period of very rapid, quasi-exponential expansion. While the time-scale for this period of expansion was far shorter than that of the current expansion, this was a period of accelerated expansion with some similarities to the current epoch.

Technical definition

The definition of "accelerating expansion" is that the second time derivative of the cosmic scale factor, ddot{a} , is positive, which implies that the deceleration parameter is negative. However, note this does not imply that the Hubble parameter is increasing with time. Since the Hubble parameter is defined as H(t) equiv dot{a}(t) / a(t) , it follows from the definitions that the derivative of the Hubble parameter is given by

frac{dH}{dt} = -H^2(1 + q)

so the Hubble parameter is decreasing with time unless q < -1 . Observations prefer q approx -0.55 , which implies that ddot{a} is positive but dH/dt is negative. Essentially, this implies that the cosmic recession velocity of any one particular galaxy is increasing with time, but its velocity/distance ratio is still decreasing; thus different galaxies expanding across a sphere of fixed radius cross the sphere more slowly at later times.It is seen from above that the case of "zero acceleration/deceleration" corresponds to a(t) is a linear function of t, q = 0 , dot{a} = const, and H(t) = 1/t .

Evidence for acceleration

To learn about the rate of expansion of the universe we look at the magnitude-redshift relationship of astronomical objects using standard candles, or their distance-redshift relationship using standard rulers. We can also look at the growth of large-scale structure, and find that the observed values of the cosmological parameters are best described by models which include an accelerating expansion.

Supernova observation

(File:Asymmetric Ashes (artist's impression).jpg|thumb|left|200px|Artist's impression of a Type Ia supernova, as revealed by spectro-polarimetry observations)The first evidence for acceleration came from the observation of Type Ia supernovae, which are exploding white dwarfs that have exceeded their stability limit. Because they all have similar masses, their intrinsic luminosity is standardizable. Repeated imaging of selected areas of the sky is used to discover the supernovae, then follow-up observations give their peak brightness, which is converted into a quantity known as luminosity distance (see distance measures in cosmology for details).ARXIV, Albrecht, Andreas, etal, Report of the Dark Energy Task Force, 2006, astro-ph/0609591, Spectral lines of their light can be used to determine their redshift.For supernovae at redshift less than around 0.1, or light travel time less than 10 percent of the age of the universe, this gives a nearly linear distanceâredshift relation due to Hubble's law. At larger distances, since the expansion rate of the universe has changed over time, the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time. The full calculation requires computer integration of the Friedmann equation, but a simple derivation can be given as follows: the redshift {{mvar|z}} directly gives the cosmic scale factor at the time the supernova exploded.

Baryon acoustic oscillations

In the early universe before recombination and decoupling took place, photons and matter existed in a primordial plasma. Points of higher density in the photon-baryon plasma would contract, being compressed by gravity until the pressure became too large and they expanded again.{{Page needed|date=September 2016}} This contraction and expansion created vibrations in the plasma analogous to sound waves. Since dark matter only interacts gravitationally it stayed at the centre of the sound wave, the origin of the original overdensity. When decoupling occurred, approximately 380,000 years after the Big Bang,JOURNAL, Hinshaw, G., 2009, Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results, 10.1088/0067-0049/180/2/225, Astrophysical Journal Supplement, 180, 2, 225â245, 0803.0732, 2009ApJS..180..225H, photons separated from matter and were able to stream freely through the universe, creating the cosmic microwave background as we know it. This left shells of baryonic matter at a fixed radius from the overdensities of dark matter, a distance known as the sound horizon. As time passed and the universe expanded, it was at these anisotropies of matter density where galaxies started to form. So by looking at the distances at which galaxies at different redshifts tend to cluster, it is possible to determine a standard angular diameter distance and use that to compare to the distances predicted by different cosmological models.Peaks have been found in the correlation function (the probability that two galaxies will be a certain distance apart) at {{nowrap|100 hâ1 Mpc}}, indicating that this is the size of the sound horizon today, and by comparing this to the sound horizon at the time of decoupling (using the CMB), we can confirm the accelerated expansion of the universe.JOURNAL, Eisenstein, Daniel J., etal, Detection of the Baryon Acoustic Peak in the LargeâScale Correlation Function of SDSS Luminous Red Galaxies, The Astrophysical Journal, 2005, 633, 2, 560â574, 10.1086/466512, 2005ApJ...633..560E, astro-ph/0501171,

Age of the universe

{{see also|Age of the universe}}Given a cosmological model with certain values of the cosmological density parameters, it is possible to integrate the Friedmann equations and derive the age of the universe.

t_0=int_{0}^{1}frac{da}{dot{a}}

By comparing this to actual measured values of the cosmological parameters, we can confirm the validity of a model which is accelerating now, and had a slower expansion in the past.

Gravitational waves as standard sirens

Recent discoveries of gravitational waves through LIGO and VIRGO JOURNAL, The LIGO Scientific Collaboration and The Virgo Collaboration, The 1M2H Collaboration, The Dark Energy Camera GW-EM Collaboration and the DES Collaboration, The DLT40 Collaboration, The Las Cumbres Observatory Collaboration, The VINROUGE Collaboration, The MASTER Collaboration, 2017-11-02, A gravitational-wave standard siren measurement of the Hubble constant,weblink Nature, 551, 7678, 85â88, 10.1038/nature24471, 29094696, 0028-0836, 1710.05835, 2017Natur.551...85A, JOURNAL, Abbott, B. P., LIGO Scientific Collaboration and Virgo Collaboration, 2016-02-11, Observation of Gravitational Waves from a Binary Black Hole Merger, Physical Review Letters, 116, 6, 061102, 10.1103/PhysRevLett.116.061102, 26918975, 1602.03837, 2016PhRvL.116f1102A, JOURNAL, ur Rahman, Syed Faisal, 2018-04-01, Where next for the expanding universe?,weblink Astronomy & Geophysics, en, 59, 2, 2.39â2.42, 10.1093/astrogeo/aty088, 1366-8781, 2018A&G....59b2.39F, not only confirmed Einstein's predictions but also opened a new window into the universe. These gravitational waves can work as sort of standard sirens to measure the expansion rate of the universe. Abbot et al. 2017 measured the Hubble constant value to be approximately 70 kilometres per second per megaparsec. The amplitudes of the strain 'h' is dependent on the masses of the objects causing waves, distances from observation point and gravitational waves detection frequencies. The associated distance measures are dependent on the cosmological parameters like the Hubble Constant for nearby objects and will be dependent on other cosmological parameters like the dark energy density, matter density, etc. for distant sources.JOURNAL, Rosado, Pablo A., Lasky, Paul D., Thrane, Eric, Zhu, Xingjiang, Mandel, Ilya, Sesana, Alberto, 2016, Detectability of Gravitational Waves from High-Redshift Binaries, Physical Review Letters, 116, 10, 101102, 10.1103/PhysRevLett.116.101102, 27015470, 1512.04950, 2016PhRvL.116j1102R,

Explanatory models

(File:Dark Energy.jpg|thumb|right|400px|The expansion of the Universe accelerating. Time flows from bottom to top)

Dark energy

The most important property of dark energy is that it has negative pressure (repulsive action) which is distributed relatively homogeneously in space.

Theories for the consequences to the universe

{{See also|Future of an expanding universe}}As the universe expands, the density of radiation and ordinary dark matter declines more quickly than the density of dark energy (see equation of state) and, eventually, dark energy dominates. Specifically, when the scale of the universe doubles, the density of matter is reduced by a factor of 8, but the density of dark energy is nearly unchanged (it is exactly constant if the dark energy is a cosmological constant).{{Page needed|date=September 2016}}In models where dark energy is a cosmological constant, the universe will expand exponentially with time in the far future, coming closer and closer to a de Sitter spacetime. This will eventually lead to all evidence for the Big Bang disappearing, as the cosmic microwave background is redshifted to lower intensities and longer wavelengths. Eventually its frequency will be low enough that it will be absorbed by the interstellar medium, and so be screened from any observer within the galaxy. This will occur when the universe is less than 50 times its current age, leading to the end of cosmology as we know it as the distant universe turns dark.JOURNAL, Krauss, Lawrence M., Scherrer, Robert J., The return of a static universe and the end of cosmology, General Relativity and Gravitation, 2007, 39, 10, 1545â1550, 10.1007/s10714-007-0472-9, 0704.0221, 2007GReGr..39.1545K, A constantly expanding universe with non-zero cosmological constant has mass density decreasing over time, to an undetermined point when zero matter density is reached. All matter (electrons, protons and neutrons) would ionize and disintegrate, with objects dissipating away.John Baez, "The End of the Universe", 7 February 2016.weblink for the ultimate fate of the universe include the Big Rip mentioned above, a Big Bounce, Big Freeze or Big Crunch.